The phase rule

The Phase Rule

1. Phase Equilibria andthe
Phase Rule
The phase
The phase diagram
The Gibbs phase rule
One component system
Two component system (liquid phases)
Two component system (solid/liquid phases)
Three component systems (liquid phases)

2. Thephase
Definition
Aphaseisthepartwhosephysicalandchemicalproperties
arecompletelyequalandhomogenous.itisseparated
fromotherpartsofthesystembyinterfaces.
Asystemcontainingwaterand
itsvaporisatwo-phase
system.Anequilibrium
mixtureofice,liquidwater,
andwatervaporisathree-
phasesystem.

3. Thephase
Definition
A phase may be gas, liquid orsolid.
A gas or a gaseous mixture is a single phase.
Completely miscible liquids constitute a singlephase.
In an immiscible liquid system, each layer is counted as a
separatephase.
Every solid constitutes a single phase except when a solid
solution isformed.
A solid solution is considered as a single phase.
Each polymorphic form constitutes a separatephase.

4. Thephase
Examples
How many phases in each of the followingsystems?
1.Liquid water, pieces of ice and water vapor are present
together.
Number of phases =3
2.CalciumCarbonateundergoesthermaldecomposition.
CaCO
3 (s) → CaO (s) + CO
2(g)
Number of phases =3
3.A solution of NaCl inwater
Number of phases =1
4.Liquid water + watervapor
Number of phases =2
5.Liquid water + water vapor +air
Number of phases =2

5. The phasediagram
Phasediagram(alsoknownasEquilibriumDiagrams)showsthe
multisystemstatechangeswiththetemperature,pressure,
compositionandotherintensiveproperties.
Thesimplestphasediagrams
arepressure-temperature
diagramsofasingle
simplesubstance.
Theaxescorrespondtothe
pressureandtemperature.
Thelinesinthephase
diagramrepresenttwo
phasesystems,whileThe
spacesbetweenthelines
representonephase
systems.

6. The Gibbs phaserule
Tounderstandanddefinethestateofaphase,knowledge
ofseveralindependentvariablesisrequired.
Independentvariables(alsocalledIntensivevariables)are
thevariablesthatdonotdependonthevolumeorsizeof
thephase,e.g.temperature,pressure,density,boiling
pointandconcentration.
TheGibbsphaseruleisexpressedasfollows:
F=C–P+2
Fisthenumberofdegreesoffreedomofthesystemwhich
istheleastnumberofintensivevariablesrequiredto
definethesystemcompletely.
C:numberofcomponents,P:numberofphasespresent

7. One componentsystem
The Gibbs phaserule
Consideraonecomponentsystemcomposedofaliquid
withparticularvolume.Usingthephaserule:
F=1-1+2=2(the
maximumnumberof
degreeoffreedom
foronecomponent
system)
Onlytwoindependent
variablesarerequired
todefinethesystem
(temperatureand
pressure)

8. One componentsystem
The Gibbs phaserule
Foraonecomponentsystemcomprisingaliquidandits
vapor. The phase rule statesthat:
F=1-2+2=1
Onlyoneindependent
variableisrequiredto
definethissystem
(eithertemperatureor
pressure)

9. One componentsystem
The Gibbs phase rule
For a one component system composed of solid, liquid, and
vapor. The phase rule statesthat:
F=1-3+2=0
Therearenodegreesof
freedom.Theice–
water–vaporsystem
iscompletelydefined
(thetemperatureand
pressureisfixedata
pointcalledthetriple
point).

10. One componentsystem
The phasediagram
O
A
B
C
ThecurveOAinthephasediagramofonecomponentsystem
representsthevaporpressurecurvewherevaporandliquidcoexist
inequilibrium.
ThecurveOBrepresentsthe
meltingcurvewherethe
solidandliquidphases
coexistinequilibrium.
ThecurveOCrepresentsthe
sublimationcurvewhere
thesolidandvaporphases
coexistinequilibrium.
Thespacesbetweenthe
curvesrepresentareaof
onephasesystem

11. One componentsystem
The phasediagram
Thecriticalpointisthepointonaphasediagramthatindicatesthe
criticaltemperatureandpressure.Whilethetriplepointrepresents
thetemperatureandpressurewhereallthreephysicalstatesarein
equilibrium.
B
A
O
C

12. One componentsystem
The phase diagram ofwater
Formostsubstancesthesolidisdenserthantheliquid.
Therefore;anincreaseinpressureusuallyfavorsthe
moredensesolidphase.
Thefrozenstateofwater(ice)isactuallylessdensethan
theliquidstate.Therefore;increasingpressure(which
favorscompactnessofthemolecules)willfavorthe
liquidstate.

13. One componentsystem
The phase diagram ofwater
The melting curve (OB) slopes to the left, unlike mostcompounds.
ThenegativeslopeofOBshowsthatthefreezingpointofwater
decreases with increasing externalpressure
Atatemperaturebelowthe
triplepoint,anincreaseof
pressureonwaterinthe
vaporstateconvertsthe
vaporfirsttoiceandthenat
higherpressureintoliquid
water.Why?

14. Two componentsystems
containing liquidphases
Systemscontainingmorethanonecomponentarebest
discussedascondensedsystems
Condensedsystemsaresystemsinwhichthevapourphase
isignoredandonlysolidandliquidphasesareconsidered.
Systemscontainingliquidsoftenareclassifiedas
1.Completelyimmiscible(suchasmercuryandwater)(not
concern)
2.Completely miscible in all proportions (e.g. ethanol and
water), (solution)
3.Partially miscible (e.g. diethyl ether and water).
(considered)

15. Two componentsystems
containing liquidphases
For two componentsystems:
C =2F = C –P+2⟹ F = 4 –P
P = 1 at least, so F is 3 atmost
Threevariablesarerequired:temperature,pressure,and
composition.
If the pressure isfixed:
C =2F = C –P +1 ⟹ F = 3 -P
P = 1 at least, so F is 2 atmost
Only are temperature and composition arerequired:

16. Two componentsystems
containing liquidphases
Phasediagramsfortwo
componentsystemsare
commonlyconstructed
withtemperatureand
compositionasthe
coordinates.
Usuallythecomposition
isexpressedasmole
fractionoraspercent
byweight(%w/w).
Why?

17. Two component systems containing
solid and liquidphases
Two component system consisting of two solids D and E brought to a
temperature above the melting points of both (pointd).
Aone-phasesystemwill
formconsistingofa
liquidsolutionofDand
E.
ThepointsofDandE
representthemelting
pointsofDandE.
Whenthetemperaturefall
topointc,puresolidE
willformdispersedina
solutionofDandE.

18. Two component systemscontaining
solid and liquidphases
AtpointGsolidD,solidEandsolutionphaseareinmutual
equilibrium (existtogether).
Thesolidphaseatthis
pointisafinelydivided
two-phasedispersionof
crystallineDandE
calledaeutectic,andG
istheeutecticpoint.
Eutecticmeltsata
lowertemperaturethan
eitherofitspure
components.

19. Three componentsystem
containing liquidphases
For three componentsystems:
C =3, P = 1 at least
F =C –P + 2
F = 3 -P + 2 = 5 –P
so F is 4 atmost
Four variables are required: temperature, pressure, and two
composition.
If the temperature and pressure is bothfixed:
C =3F = C -P ⟹ F = 3 -P
P = 1 at least, so F is 2 at most
Only two composition isrequired.

20. Three componentsystem
containing liquidphases
Phasediagramsare
commonlyconstructed
onequilateraltriangle
withthreepeaksthat
separatelystandsfor
purecompositionA,B
andC.

21. Reference
Sinko,Martin'sphysicalpharmacyandpharmaceuticalsciences:physical
chemicalandbiopharmaceuticalprinciplesinthepharmaceuticalsciences,
Philadelphia,LippincottWilliams&Wilkins.